Can not import Blender animation into Unity
Unity uses Blender's FBX export functionality to throw your model over the wall to Unity.  The FBX file spec only allows for Meshes (and derivatives thereof, such as bones and bone weights), Animations of Meshes, Materials, and Textures, and Blender's FBX implementation is incomplete.  Right now, there is no way to export bezier animations directly.

You could, theoretically, export your animations by binding your animation to an armature, exporting the armature to Unity through FBX, and using a plugin like Bezier Mesh to render the curve and parenting it's controls to your imported mesh.  This is pure speculation on my part, though.